Question: Rewrite as a simplified fraction. ${0.1\overline{7} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 17.7777...\\ 10x &= 1.7777...\end{align*}}$ Subtracting the two equations, we have: ${90x = 16}$ ${x = \dfrac{16}{90}} $ ${x = \dfrac{8}{45}} $